(5x^2-10x)+(-8x+82)=90

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Solution for (5x^2-10x)+(-8x+82)=90 equation: 


Simplifying
(5x2 + -10x) + (-8x + 82) = 90

Reorder the terms:
(-10x + 5x2) + (-8x + 82) = 90

Remove parenthesis around (-10x + 5x2)
-10x + 5x2 + (-8x + 82) = 90

Reorder the terms:
-10x + 5x2 + (82 + -8x) = 90

Remove parenthesis around (82 + -8x)
-10x + 5x2 + 82 + -8x = 90

Reorder the terms:
82 + -10x + -8x + 5x2 = 90

Combine like terms: -10x + -8x = -18x
82 + -18x + 5x2 = 90

Solving
82 + -18x + 5x2 = 90

Solving for variable 'x'.

Reorder the terms:
82 + -90 + -18x + 5x2 = 90 + -90

Combine like terms: 82 + -90 = -8
-8 + -18x + 5x2 = 90 + -90

Combine like terms: 90 + -90 = 0
-8 + -18x + 5x2 = 0

Factor a trinomial.
(-2 + -5x)(4 + -1x) = 0


Subproblem 1
Set the factor '(-2 + -5x)' equal to zero and attempt to solve:

Simplifying
-2 + -5x = 0

Solving
-2 + -5x = 0

Move all terms containing x to the left, all other terms to the right.

Add '2' to each side of the equation.
-2 + 2 + -5x = 0 + 2

Combine like terms: -2 + 2 = 0
0 + -5x = 0 + 2
-5x = 0 + 2

Combine like terms: 0 + 2 = 2
-5x = 2

Divide each side by '-5'.
x = -0.4

Simplifying
x = -0.4

Subproblem 2
Set the factor '(4 + -1x)' equal to zero and attempt to solve:

Simplifying
4 + -1x = 0

Solving
4 + -1x = 0

Move all terms containing x to the left, all other terms to the right.

Add '-4' to each side of the equation.
4 + -4 + -1x = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1x = 0 + -4
-1x = 0 + -4

Combine like terms: 0 + -4 = -4
-1x = -4

Divide each side by '-1'.
x = 4

Simplifying
x = 4
Solution
x = {-0.4, 4}

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